General theoretical formulation of image formation in digital Fresnel holography.

We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences.

Tracking high amplitude auto-oscillations with digital Fresnel holograms.

Method for tracking vibrations with high amplitude of several hundreds of micrometers is presented. It is demonstrated that it is possible to reconstruct a synthetic high amplitude deformation of auto-oscillations encoded with digital Fresnel holograms. The setup is applied to the auto-oscillation of a clarinet reed in a synthetic mouth.

2D full field vibration analysis with multiplexed digital holograms.

Opportunities for full field 2D amplitude and phase vibration analysis are presented. It is demonstrated that it is possible to simultaneously encode-decode 2D the amplitude and phase of harmonic mechanical vibrations. The process allows the determination of in plane and out of plane vibration components when the object is under a pure sinusoidal excitation.

Full-field vibrometry with digital Fresnel holography.

A setup that permits full-field vibration amplitude and phase retrieval with digital Fresnel holography is presented. Full reconstruction of the vibration is achieved with a three-step stroboscopic holographic recording, and an extraction algorithm is proposed. The finite temporal width of the illuminating light is considered in an investigation of the distortion of the measured amplitude and phase.

Some opportunities for vibration analysis with time averaging in digital Fresnel holography.

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts.

Time-averaged digital holography.

We demonstrate that it is possible to study the modal structures of a vibrating object with digitally recorded holograms by use of the time-averaging principle. We investigate the numerical reconstruction from a theoretical point of view, and we show that the numerically reconstructed object from a digital hologram is modulated by the zeroth-order Bessel function. Results of experiments in time-averaged digital holography are presented.